3 sin ⁡ x − cos ⁡ x = 2 I think to do : ( 3 sin ⁡ x − cos ⁡ x = 2 ) 2 but i dont get anything. Or to divied by 3 : ( 3 sin ⁡ x − cos ⁡ x = 2 ) 3

Question

3    sin  ⁡      x    −  cos  ⁡      x    =      2  I think to do :            (              3            sin      ⁡              x            −      cos      ⁡              x            =              2            )              2      but i dont get anything. Or to divied by       3   :            (              3            sin      ⁡              x            −      cos      ⁡              x            =              2            )              3

barquegese2 · Accepted Answer

Hint:      3    sin  ⁡  x  −  cos  ⁡  x  =      2      ⟺    sin  ⁡      π    3    sin  ⁡  x  −  cos  ⁡      π    3    cos  ⁡  x  =            2        2

tonan6e · Accepted Answer

One of the R-Formulas, a set of formulas for combining such trigonometric expressions, says that  a  sin  ⁡      x    −  b  cos  ⁡      x    =  R  sin  ⁡  (  x  −  α  )where  R  =            a      2        +          b      2        ,  α  =      tan          −      1        ⁡            b      a      However, I doubt this solution expresses any room for creativity for this question specifically, as noted by first answer

solve a trigonometric equation sqrt(3) sin(x)−cos(x)=sqrt(2)

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